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The Igloo Cube is about 12x12x12. (Although, according to the Igloo website, it's really 12.56"L x 12.25"W x 11.75"H.) But it would be easier to just get a soft sided one and put it in your luggage so you don't have to worry about it.

On ships without mini fridges we carry the Coleman Lil' Oscar cooler (don't know if they still make this model, we have had this one for a while). It is smaller than 12 x 12 x 12. It is about 12 x 10 x 8 and will hold about 8 12 oz. cans.

Got ours at Wallyworld......
It's probably a little smaller than 12x12x12, but it was big enough to hold 11 cans (yeah, I know, why not 1 more to finish the 12-pack?) of Dr. Pepper in it. No ice yet, of course.
We taped it shut with duct tape, but not too much, so they could open it easily to check it. Even threw in the roll of duct tape in case it needed more taping.
We put a checked luggage tag on it and handed it to the porter at the ship terminal with our other checked luggage and it was delivered to our stateroom. It was nice not having to carry it on.
Our steward kept it full of ice all week.
Sorry I don't have a photo. It's being borrowed right now.

Yes, they are that picky! I had check-in take out a tape measure and I was 1/2 inch over and we ended up taking it back to the car. Take a soft side and pack it in your luggage!
That is what we will be doing on 9/12 on the Inspiration!!

Yes, We had a soft sided cooler that we bought at Costco that was about 14"x14"x14" and we were stopped and had to remove all the sodas and put them in our luggage, collapse the bag, throw away the ice and fit the bag in our luggage or they (Security at the port) was going to "throw away" our new cooler. All that hassle for a bag that was a little bigger than the 12"x12". And to top it off they (security) were all a$*holes.

Found an "expandable hardcore cooler" at WalMart for $12.88. Made by Arctic Zone and is approximately 12x12x6 with a padded shoulder strap. It is soft but has a plastic insert that pretty much guarantees no leaking. The label says it will hold 16 cans with ice. I plan on putting items such as extension cord, night light, snacks, etc., inside and checking it.

I have heard that the soft-side leak, do they
Worried about having it on the floor in the cabin if it leaks.
I think I read that people keep it in the shower or on the balcony.

Our softsided started to leak a bit after 2 days due to condensation. We dumped the ice out a couple times so the RS didn't have to do it, and she just kept refilling it with more ice. We had it on the carpet with a towel underneath. Worked perfectly for our soda, water, pineapple juice and other goodies.